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 A192857 Number of matchings in the n-web graph. 1
 4, 3, 23, 93, 439, 1988, 9107, 41583, 190047, 868341, 3967828, 18130335, 82844095, 378544117, 1729703523, 7903633148, 36114524127, 165020163823, 754036089983, 3445460307689, 15743539192644, 71937855657915, 328709765539959, 1501992365110237, 6863139770575695, 31360137777380788 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Extended to a(0)-a(2) using the recurrence. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 (corrected by Ray Chandler, Jan 19 2019) Eric Weisstein's World of Mathematics, Independent Edge Set Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Web Graph Wikipedia, Hosoya index Index entries for linear recurrences with constant coefficients, signature (3,7,1,-1). FORMULA G.f.: (1+x)*(4 - 13*x - x^2)/(1 - 3*x - 7*x^2 - x^3 + x^4). MATHEMATICA LinearRecurrence[{3, 7, 1, -1}, {4, 3, 23, 93, 439}, 30] (* Eric W. Weisstein, Mar 09 2016; amended for a(0) by Georg Fischer, Apr 03 2019 *) Table[RootSum[1 - # - 7 #^2 - 3 #^3 + #^4 &, #^n &], {n, 0, 30}] (* Eric W. Weisstein, May 25 2017; amended for a(0) by Georg Fischer, Apr 03 2019 *) RootSum[1 - # - 7 #^2 - 3 #^3 + #^4 &, #^Range[0, 30] &] (* Eric W. Weisstein, Oct 03 2017 *) CoefficientList[Series[(4-9x-14x^2-x^3)/(1-3x-7x^2-x^3+x^4), {x, 0, 30}], x] (* Eric W. Weisstein, Oct 03 2017 *) PROG (PARI) polsym(x^4 - 3*x^3 - 7*x^2 - x + 1, 30) \\ Joerg Arndt, May 26 2017 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1+x)*(4-13*x-x^2)/(1-3*x-7*x^2-x^3+x^4) )); // G. C. Greubel, Jan 06 2019 (Sage) ((1+x)*(4-13*x-x^2)/(1-3*x-7*x^2-x^3+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 06 2019 CROSSREFS Sequence in context: A052039 A243661 A035048 * A286671 A288434 A288011 Adjacent sequences:  A192854 A192855 A192856 * A192858 A192859 A192860 KEYWORD nonn AUTHOR Eric W. Weisstein, Jul 11 2011 EXTENSIONS Redefined to include all web graphs, a(9)-a(25) from Andrew Howroyd, Mar 08 2016 Extended to a(0)-a(2) using recurrence by Eric W. Weisstein, May 26 2017 STATUS approved

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Last modified September 20 02:19 EDT 2021. Contains 347577 sequences. (Running on oeis4.)